Robust estimation of efficient mean–variance frontiers

Standard methods for optimal allocation of shares in a financial portfolio are determined by second-order conditions which are very sensitive to outliers. The well-known Markowitz approach, which is based on the input of a mean vector and a covariance matrix, seems to provide questionable results in financial management, since small changes of inputs might lead to irrelevant portfolio allocations. However, existing robust estimators often suffer from masking of multiple influential observations, so we propose a new robust estimator which suitably weights data using a forward search approach. A Monte Carlo simulation study and an application to real data show some advantages of the proposed approach.

[1]  Francisco J. Nogales,et al.  Portfolio Selection With Robust Estimation , 2007, Oper. Res..

[2]  Richard O. Michaud.  The Markowitz Optimization Enigma: Is 'Optimized' Optimal? , 1989 .

[3]  Xinfeng Zhou,et al.  Application of robust statistics to asset allocation models , 2006 .

[4]  Roy E. Welsch,et al.  Robust Portfolio Optimization , 2002 .

[5]  A. Atkinson.  Fast Very Robust Methods for the Detection of Multiple Outliers , 1994 .

[6]  Katrien van Driessen,et al.  A Fast Algorithm for the Minimum Covariance Determinant Estimator , 1999, Technometrics.

[7]  Anthony C. Atkinson,et al.  The forward search: theory and data analysis , 2010 .

[8]  A. Atkinson,et al.  Finding an unknown number of multivariate outliers , 2009 .

[9]  Anthony C. Atkinson,et al.  Robust Diagnostic Regression Analysis , 2000 .

[10]  H. Markowitz.  Portfolio Selection: Efficient Diversification of Investments , 1971 .

[11]  A. Stuart,et al.  Portfolio Selection: Efficient Diversification of Investments , 1959 .

[12]  Peter J. Rousseeuw,et al.  Robust Regression and Outlier Detection , 2005, Wiley Series in Probability and Statistics.

[13]  Christine M. Anderson-Cook,et al.  Book review: quantitative risk management: concepts, techniques and tools, revised edition, by A.F. McNeil, R. Frey and P. Embrechts. Princeton University Press, 2015, ISBN 978-0-691-16627-8, xix + 700 pp. , 2017, Extremes.

[14]  P. Rousseeuw,et al.  A fast algorithm for the minimum covariance determinant estimator , 1999 .

[15]  M. Fukushima,et al.  Portfolio selection with uncertain exit time: A robust CVaR approach , 2008 .

[16]  S. Zani,et al.  Robust bivariate boxplots and multiple outlier detection , 1998 .

[17]  Richard O. Michaud,et al.  The Markowitz Optimization Enigma: Is ‘Optimized’ Optimal? , 2005 .

[18]  Alfio Marazzi,et al.  Algorithms, Routines, and s Functions for Robust Statistics: The Fortran Library Robeth With an Interface to S-Plus , 1993 .

[19]  Anthony C. Atkinson,et al.  Exploring Multivariate Data with the Forward Search , 2004 .

[20]  Mark Broadie,et al.  Computing efficient frontiers using estimated parameters , 1993, Ann. Oper. Res..

[21]  Luigi Grossi,et al.  A robust forward weighted Lagrange multiplier test for conditional heteroscedasticity , 2009, Comput. Stat. Data Anal..

[22]  Alexandre M. Baptista,et al.  Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-variance analysis , 2002 .